{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "name": "quantile_regression_comparison_cps.ipynb", "version": "0.3.2", "provenance": [], "collapsed_sections": [], "include_colab_link": true }, "kernelspec": { "name": "python3", "display_name": "Python 3" } }, "cells": [ { "cell_type": "markdown", "metadata": { "id": "view-in-github", "colab_type": "text" }, "source": [ "[View in Colaboratory](https://colab.research.google.com/github/MaxGhenis/taxcalc-notebooks/blob/master/quantile_regression_comparison_cps.ipynb)" ] }, { "metadata": { "id": "zricQzqlyPYk", "colab_type": "toc" }, "cell_type": "markdown", "source": [ ">[Quantile regression from OLS to TensorFlow](#scrollTo=PQdJbWCS9N3G)\n", "\n", ">>[Setup](#scrollTo=VjvK4vP2-X_D)\n", "\n", ">>>[Graph options](#scrollTo=sm3RTN850S70)\n", "\n", ">>>[Data](#scrollTo=vdaqXkSCe7gG)\n", "\n", ">>>>[Load](#scrollTo=vdaqXkSCe7gG)\n", "\n", ">>>>[Randomize and split](#scrollTo=80yZ1lihmLQq)\n", "\n", ">>>>[Normalize](#scrollTo=xuphFNDqtEiW)\n", "\n", ">>>[Initialize result](#scrollTo=utzAT-gdBTqj)\n", "\n", ">>[OLS](#scrollTo=6dRLoTDhCrpO)\n", "\n", ">>[QuantReg](#scrollTo=esTAKyTyG1TS)\n", "\n", ">>[Random forests](#scrollTo=qCt2S4V9Uepc)\n", "\n", ">>[Gradient boosted trees](#scrollTo=6ssXXxsCA7FS)\n", "\n", ">>[Keras](#scrollTo=H55y_74W97jH)\n", "\n", ">>[TensorFlow](#scrollTo=PEy2M6X89tbD)\n", "\n", ">>[Compare quantile loss](#scrollTo=42LIBXl933YI)\n", "\n" ] }, { "metadata": { "id": "PQdJbWCS9N3G", "colab_type": "text" }, "cell_type": "markdown", "source": [ "# Quantile regression from OLS to TensorFlow\n", "\n", "Use the [CPS data.](https://github.com/open-source-economics/taxdata/blob/master/cps_data/cps.csv.gz)\n", "\n", "Based on blog posts using:\n", "* Keras: https://towardsdatascience.com/deep-quantile-regression-c85481548b5a\n", "* Tensorflow: https://towardsdatascience.com/deep-quantile-regression-in-tensorflow-1dbc792fe597\n", "* statsmodels quantile regression: https://www.statsmodels.org/dev/examples/notebooks/generated/quantile_regression.html" ] }, { "metadata": { "id": "VjvK4vP2-X_D", "colab_type": "text" }, "cell_type": "markdown", "source": [ "## Setup" ] }, { "metadata": { "id": "yf26Fpx3-H-Y", "colab_type": "code", "colab": { "base_uri": "https://localhost:8080/", "height": 51 }, "outputId": "7e8d6132-aed4-4fbf-b130-2ea20a289239" }, "cell_type": "code", "source": [ "import pandas as pd\n", "import numpy as np\n", "\n", "import matplotlib as mpl\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "\n", "import statsmodels.api as sm\n", "\n", "from scipy.stats import norm\n", "\n", "from sklearn import ensemble\n", "from sklearn.model_selection import train_test_split\n", "from sklearn import linear_model\n", "\n", "import tensorflow as tf\n", "from tensorflow import keras" ], "execution_count": 2, "outputs": [ { "output_type": "stream", "text": [ "/usr/local/lib/python3.6/dist-packages/statsmodels/compat/pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n", " from pandas.core import datetools\n" ], "name": "stderr" } ] }, { "metadata": { "id": "VrIWCe8L1imk", "colab_type": "text" }, "cell_type": "markdown", "source": [ "Random forest and GBM options." ] }, { "metadata": { "id": "-r1h-uzW1lC3", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "N_ESTIMATORS = 200" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "oBg62ioP8v0l", "colab_type": "text" }, "cell_type": "markdown", "source": [ "Keras and TensorFlow options" ] }, { "metadata": { "id": "SWyQCM_S8xvp", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "EPOCHS = 20\n", "BATCH_SIZE = 32\n", "UNITS = 64" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "sm3RTN850S70", "colab_type": "text" }, "cell_type": "markdown", "source": [ "### Graph options" ] }, { "metadata": { "id": "2x4nw9Pm1r6S", "colab_type": "code", "colab": { "base_uri": "https://localhost:8080/", "height": 51 }, "outputId": "baec6a25-b453-484d-90df-88e667746445" }, "cell_type": "code", "source": [ "!wget https://github.com/MaxGhenis/random/raw/master/Roboto-Regular.ttf -P /usr/local/lib/python3.6/dist-packages/matplotlib/mpl-data/fonts/ttf\n", "mpl.font_manager._rebuild()" ], "execution_count": 5, "outputs": [ { "output_type": "stream", "text": [ "\n", "Redirecting output to ‘wget-log’.\n" ], "name": "stdout" } ] }, { "metadata": { "id": "Nhth3s2j0VIK", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "sns.set_style('white')\n", "DPI = 200\n", "mpl.rc('savefig', dpi=DPI)\n", "mpl.rcParams['figure.dpi'] = DPI\n", "mpl.rcParams['figure.figsize'] = 6.4, 4.8 # Default.\n", "mpl.rcParams['font.sans-serif'] = 'Roboto'\n", "mpl.rcParams['font.family'] = 'sans-serif'\n", "\n", "# Set title text color to dark gray (https://material.io/color) not black.\n", "TITLE_COLOR = '#212121'\n", "mpl.rcParams['text.color'] = TITLE_COLOR\n", "\n", "# Axis titles and tick marks are medium gray.\n", "AXIS_COLOR = '#757575'\n", "mpl.rcParams['axes.labelcolor'] = AXIS_COLOR\n", "mpl.rcParams['xtick.color'] = AXIS_COLOR\n", "mpl.rcParams['ytick.color'] = AXIS_COLOR" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "vdaqXkSCe7gG", "colab_type": "text" }, "cell_type": "markdown", "source": [ "### Data\n", "\n", "#### Load" ] }, { "metadata": { "id": "mZ5Ic69nk1OH", "colab_type": "code", "colab": { "base_uri": "https://localhost:8080/", "height": 51 }, "outputId": "2db8309e-0d7a-4002-851e-8f50aef5e6aa" }, "cell_type": "code", "source": [ "!wget -N https://github.com/open-source-economics/taxdata/raw/master/cps_data/cps.csv.gz\n", "!gunzip -f cps.csv.gz" ], "execution_count": 7, "outputs": [ { "output_type": "stream", "text": [ "\n", "Redirecting output to ‘wget-log.1’.\n" ], "name": "stdout" } ] }, { "metadata": { "id": "6DX58bWylfOC", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "raw = pd.read_csv('cps.csv')" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "SJhy87dDRHOU", "colab_type": "text" }, "cell_type": "markdown", "source": [ "### Preprocess\n", "\n", "Select only common variables." ] }, { "metadata": { "id": "ZuuydcoblEmZ", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "TARGET = 'e00900'" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "Y4GGDAsYFHoL", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "dat = raw.copy(deep=True)" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "gOunEKiEFN8z", "colab_type": "text" }, "cell_type": "markdown", "source": [ "Feature engineering." ] }, { "metadata": { "id": "jLeBHgDvRON9", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "# CPS data has MARS values of 1, 2, and 4.\n", "dat[['MARS2', 'MARS4']] = pd.get_dummies(dat.MARS, drop_first=True)" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "se5-Q9-YSZcp", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "dat['e19800_e20100'] = dat.e19800 + dat.e20100" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "-5PrkL6RRI97", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "PREDICTORS = ['DSI', 'EIC', 'MARS2', 'MARS4', 'XTOT', \n", " 'e00200', 'e00300', 'e00400', 'e00600', 'e00800',\n", " 'e01400', 'e01500', 'e01700', 'e02100', 'e02300', 'e02400', \n", " 'e03150', 'e03210', 'e03240', 'e03270', 'e03300', 'e17500', \n", " 'e18400', 'e18500', 'e19200', 'e19800_e20100', 'e20400', \n", " 'e32800', 'f2441', 'n24', 'e01100']" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "dZKQQ6zOSmju", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "dat = dat[PREDICTORS + [TARGET]]" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "oI4nrhsJFdCw", "colab_type": "text" }, "cell_type": "markdown", "source": [ "Create log-transformed version. Calculate y later." ] }, { "metadata": { "id": "GXwWatLxFe9p", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "LOG_PREDICTORS = ['e00200', 'e00300', 'e00400', 'e00600', 'e00800',\n", " 'e01400', 'e01500', 'e01700', 'e02100', 'e02300', 'e02400', \n", " 'e03150', 'e03210', 'e03240', 'e03270', 'e03300', 'e17500', \n", " 'e18400', 'e18500', 'e19200', 'e19800_e20100', 'e20400', \n", " 'e32800', 'e01100']" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "T-RwPF4-Gb9I", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "for i in LOG_PREDICTORS:\n", " dat[i + '_log'] = np.log(dat[i] - dat[i].min() + 1)" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "80yZ1lihmLQq", "colab_type": "text" }, "cell_type": "markdown", "source": [ "#### Randomize and split\n", "\n", "Initial order may or may not be random." ] }, { "metadata": { "id": "qNcGS0-cprG_", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "X_train_full, X_test_full, y_train, y_test = train_test_split(\n", " dat.drop(TARGET, axis=1), dat[TARGET], test_size=0.2, random_state=42)" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "xuphFNDqtEiW", "colab_type": "text" }, "cell_type": "markdown", "source": [ "#### Normalize" ] }, { "metadata": { "id": "f4nQmq2b9H7s", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "mean = X_train_full.mean(axis=0)\n", "std = X_train_full.std(axis=0)\n", "X_train_full_std = (X_train_full - mean) / std\n", "X_test_full_std = (X_test_full - mean) / std" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "oVp-_TEuIiWZ", "colab_type": "text" }, "cell_type": "markdown", "source": [ "Separate into standard and log versions." ] }, { "metadata": { "id": "FVC8snhaIll-", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "X_train = X_train_full_std[PREDICTORS]\n", "X_test = X_test_full_std[PREDICTORS]\n", "\n", "X_train_log = X_train_full_std.drop(PREDICTORS, axis=1)\n", "X_test_log = X_test_full_std.drop(PREDICTORS, axis=1)" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "4Ho4sGWUK4gj", "colab_type": "text" }, "cell_type": "markdown", "source": [ "Reformat data for `statsmodels`." ] }, { "metadata": { "id": "3JHMdYEsK0Fy", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "X_train_w_constant = sm.add_constant(X_train)\n", "X_test_w_constant = sm.add_constant(X_test)\n", "\n", "X_train_log_w_constant = sm.add_constant(X_train_log)\n", "X_test_log_w_constant = sm.add_constant(X_test_log)" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "0b3NaFmD1Ccs", "colab_type": "text" }, "cell_type": "markdown", "source": [ "Reformat 1-column data for `tensorflow`." ] }, { "metadata": { "id": "Uw3v_o1E-TL4", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "y_train_expanded = np.expand_dims(y_train, 1)" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "rsEPQ7D5CVvY", "colab_type": "text" }, "cell_type": "markdown", "source": [ "#### Data for two-stage logit+OLS\n", "\n", "Log features." ] }, { "metadata": { "id": "mDZHkXiSCaFQ", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "y_train_sign = np.sign(y_train)\n", "y_train_pos = y_train[y_train > 0]\n", "y_train_pos_log = np.log(y_train_pos)\n", "X_train_log_w_constant_pos = X_train_log_w_constant[y_train > 0]\n", "y_train_neg = y_train[y_train < 0]\n", "y_train_neg_log = np.log(-y_train_neg)\n", "X_train_log_w_constant_neg = X_train_log_w_constant[y_train < 0]" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "utzAT-gdBTqj", "colab_type": "text" }, "cell_type": "markdown", "source": [ "### Initialize result\n", "\n", "Dataset per method, quantile, and `x` value." ] }, { "metadata": { "id": "Yl9sksV-Gqz1", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "METHODS = ['OLS', 'LogitOLS', 'QuantReg', 'Random forests', 'Gradient boosting', 'Keras',\n", " 'TensorFlow']\n", "\n", "QUANTILES = [0.1, 0.3, 0.5, 0.7, 0.9]\n", "\n", "quantiles_legend = [str(int(q * 100)) + 'th percentile' for q in QUANTILES]" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "8YjjbPaDRPgV", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "# sns.set_palette(sns.color_palette('Blues', len(QUANTILES)))\n", "sns.set_palette(sns.color_palette('Blues'))\n", "# Set dots to a light gray\n", "dot_color = sns.color_palette('coolwarm', 3)[1]" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "UTPkMtz-BlcI", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "preds = np.array([(method, q, ix) \n", " for method in METHODS \n", " for q in QUANTILES\n", " for ix in y_test.index])\n", "preds = pd.DataFrame(preds)\n", "preds.columns = ['method', 'q', 'ix']\n", "preds['label'] = np.resize(y_test, preds.shape[0])\n", "preds = preds.apply(lambda x: pd.to_numeric(x, errors='ignore'))" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "6dRLoTDhCrpO", "colab_type": "text" }, "cell_type": "markdown", "source": [ "## OLS\n", "\n", "https://stackoverflow.com/questions/17559408/confidence-and-prediction-intervals-with-statsmodels" ] }, { "metadata": { "id": "kw6TMkrSxz2K", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "ols = sm.OLS(y_train, X_train_w_constant).fit()" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "sj5U8ws6xr1G", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "def ols_quantile(m, X, q):\n", " # m: OLS model.\n", " # X: X matrix.\n", " # q: Quantile.\n", " #\n", " # Set alpha based on q. Vectorized for different values of q.\n", " mean_pred = m.predict(X)\n", " se = np.sqrt(m.scale)\n", " return mean_pred + norm.ppf(q) * se" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "J3_c9gO8MK9y", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "preds.loc[preds.method == 'OLS', 'pred'] = np.concatenate(\n", " [ols_quantile(ols, X_test_w_constant, q) for q in QUANTILES]) " ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "dcIdeWX_TRX8", "colab_type": "text" }, "cell_type": "markdown", "source": [ "## Logit + OLS\n", "\n", "Predict the sign (negative/zero/positive), then apply log regressions.\n", "\n", "See [taxdata #221](https://github.com/open-source-economics/taxdata/issues/221), [taxdata #267](https://github.com/open-source-economics/taxdata/issues/267), [taxdata #275](https://github.com/open-source-economics/taxdata/pull/275), [my notebook](http://nbviewer.jupyter.org/github/MaxGhenis/taxcalc-notebooks/blob/master/exploratory/random_forests_imputation.ipynb), and [Avi Leventhal's notebook](http://nbviewer.jupyter.org/github/Abraham-Leventhal/taxdata/blob/Abraham-Leventhal-patch-1/cps_data/Imputation%20Project/P22250%20Full%20Imputation%20RF%20vs%20mnlogitOLS.ipynb)." ] }, { "metadata": { "id": "8_sBdrjsUxOB", "colab_type": "text" }, "cell_type": "markdown", "source": [ "Segment into positive and negative.\n" ] }, { "metadata": { "id": "c5bcLQF-lHSt", "colab_type": "code", "colab": { "base_uri": "https://localhost:8080/", "height": 85 }, "outputId": "ebfbef88-fbca-415e-d3d2-d2a5e4a3693c" }, "cell_type": "code", "source": [ "mult = linear_model.LogisticRegression(\n", " multi_class='multinomial', solver='newton-cg', random_state=3)\n", "mult.fit(X_train_log, y_train_sign)" ], "execution_count": 125, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n", " intercept_scaling=1, max_iter=100, multi_class='multinomial',\n", " n_jobs=1, penalty='l2', random_state=3, solver='newton-cg',\n", " tol=0.0001, verbose=0, warm_start=False)" ] }, "metadata": { "tags": [] }, "execution_count": 125 } ] }, { "metadata": { "id": "2nhLzZucVCdd", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "ols_pos = sm.OLS(y_train_pos_log, X_train_log_w_constant_pos).fit()\n", "ols_neg = sm.OLS(y_train_neg_log, X_train_log_w_constant_neg).fit()" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "O-ccxbmpmfmr", "colab_type": "text" }, "cell_type": "markdown", "source": [ "### Predict" ] }, { "metadata": { "id": "0TR5HbRTnGbz", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "mult_probs = mult.predict_proba(X_test_log)" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "Ev_ii5i5mi3s", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "test_logit_ols = pd.DataFrame({\n", " 'neg_prob': mult_probs[:, 0],\n", " 'zero_prob': mult_probs[:, 1],\n", " 'neg_pred': ols_neg.predict(X_test_log_w_constant),\n", " 'neg_se': np.sqrt(ols_neg.scale),\n", " 'pos_pred': ols_pos.predict(X_test_log_w_constant),\n", " 'pos_se': np.sqrt(ols_pos.scale)\n", "})" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "kuit9rnyK1xE", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "def ols_q(mean, q, se):\n", " return mean + norm.ppf(q) * se" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "kPjCieienwR0", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "def mult_ols_quantile(df, q):\n", " # df: DataFrame with columns for neg_prob, zero_prob, neg_pred, neg_se, \n", " # pos_pred, and pos_se.\n", " # q: Quantile.\n", " #\n", " # Calculate the quantile within each OLS model.\n", " neg_q = q / df.neg_prob\n", " pos_q = (q - df.neg_prob - df.zero_prob) / (1 - df.neg_prob - df.zero_prob)\n", " sign = np.where(q < df.neg_prob, -1, \n", " np.where(q < (df.neg_prob + df.zero_prob), 0, 1))\n", " return np.where(sign == -1, -np.exp(ols_q(df.neg_pred, neg_q, df.neg_se)),\n", " np.where(sign == 1, \n", " np.exp(ols_q(df.pos_pred, pos_q, df.pos_se)),\n", " 0))" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "4cOiA6uos2GV", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "preds.loc[preds.method == 'LogitOLS', 'pred'] = np.concatenate(\n", " [mult_ols_quantile(test_logit_ols, q) for q in QUANTILES]) " ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "esTAKyTyG1TS", "colab_type": "text" }, "cell_type": "markdown", "source": [ "## QuantReg\n", "\n", "https://www.statsmodels.org/dev/examples/notebooks/generated/quantile_regression.html" ] }, { "metadata": { "id": "nqQsdsgxG39N", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "# Don't fit yet, since we'll fit once per quantile.\n", "quantreg = sm.QuantReg(y_train, X_train_w_constant)" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "KzSxkZpoTnr2", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "preds.loc[preds.method == 'QuantReg', 'pred'] = np.concatenate(\n", " [quantreg.fit(q=q).predict(X_test_w_constant) for q in QUANTILES]) " ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "qCt2S4V9Uepc", "colab_type": "text" }, "cell_type": "markdown", "source": [ "## Random forests" ] }, { "metadata": { "id": "0PerkzyaUgRg", "colab_type": "code", "colab": { "base_uri": "https://localhost:8080/", "height": 170 }, "outputId": "9ef8de0f-5754-4e8a-dc2d-b32610178f0c" }, "cell_type": "code", "source": [ "rf = ensemble.RandomForestRegressor(n_estimators=N_ESTIMATORS, \n", " min_samples_leaf=1, random_state=3, \n", " verbose=True, \n", " n_jobs=-1) # Use maximum number of cores.\n", "rf.fit(X_train, y_train)" ], "execution_count": 37, "outputs": [ { "output_type": "stream", "text": [ "[Parallel(n_jobs=-1)]: Done 46 tasks | elapsed: 3.8min\n", "[Parallel(n_jobs=-1)]: Done 196 tasks | elapsed: 16.0min\n", "[Parallel(n_jobs=-1)]: Done 200 out of 200 | elapsed: 16.3min finished\n" ], "name": "stderr" }, { "output_type": "execute_result", "data": { "text/plain": [ "RandomForestRegressor(bootstrap=True, criterion='mse', max_depth=None,\n", " max_features='auto', max_leaf_nodes=None,\n", " min_impurity_decrease=0.0, min_impurity_split=None,\n", " min_samples_leaf=1, min_samples_split=2,\n", " min_weight_fraction_leaf=0.0, n_estimators=200, n_jobs=-1,\n", " oob_score=False, random_state=3, verbose=True, warm_start=False)" ] }, "metadata": { "tags": [] }, "execution_count": 37 } ] }, { "metadata": { "id": "_xwAmHf4QICh", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "def rf_quantile(m, X, q):\n", " rf_preds = []\n", " for estimator in m.estimators_:\n", " rf_preds.append(estimator.predict(X))\n", " rf_preds = np.array(rf_preds).transpose() # One row per record.\n", " return np.percentile(rf_preds, q * 100, axis=1)" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "Mcza9OH6PysW", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "preds.loc[preds.method == 'Random forests', 'pred'] = np.concatenate(\n", " [rf_quantile(rf, X_test, q) for q in QUANTILES]) " ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "6ssXXxsCA7FS", "colab_type": "text" }, "cell_type": "markdown", "source": [ "## Gradient boosted trees" ] }, { "metadata": { "id": "g7s7Grj-A-Sf", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "def gb_quantile(X_train, train_labels, X, q):\n", " print(q)\n", " gbf = ensemble.GradientBoostingRegressor(loss='quantile', alpha=q,\n", " n_estimators=N_ESTIMATORS,\n", " max_depth=3,\n", " verbose=True,\n", " learning_rate=0.1, \n", " min_samples_leaf=9,\n", " min_samples_split=9)\n", " gbf.fit(X_train, train_labels)\n", " return gbf.predict(X)" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "AJLhBaTcCgZL", "colab_type": "code", "colab": { "base_uri": "https://localhost:8080/", "height": 1887 }, "outputId": "fd0537e2-37f6-4f55-c9f5-0edd82975b83" }, "cell_type": "code", "source": [ "preds.loc[preds.method == 'Gradient boosting', 'pred'] = np.concatenate(\n", " [gb_quantile(X_train, y_train, X_test, q)\n", " for q in QUANTILES])" ], "execution_count": 41, "outputs": [ { "output_type": "stream", "text": [ "0.1\n", " Iter Train Loss Remaining Time \n", " 1 1035.2734 2.26m\n", " 2 1035.2734 2.23m\n", " 3 1035.2734 2.23m\n", " 4 1035.2734 2.22m\n", " 5 1035.2734 2.22m\n", " 6 1035.2734 2.22m\n", " 7 1035.2734 2.22m\n", " 8 1035.2734 2.22m\n", " 9 1035.2734 2.21m\n", " 10 1035.2734 2.21m\n", " 20 1035.2734 2.10m\n", " 30 1035.2734 2.00m\n", " 40 1035.2734 1.90m\n", " 50 1035.2734 1.78m\n", " 60 1035.2734 1.66m\n", " 70 1035.2734 1.54m\n", " 80 1035.2734 1.42m\n", " 90 1035.2734 1.30m\n", " 100 1035.2734 1.18m\n", " 200 1035.2734 0.00s\n", "0.3\n", " Iter Train Loss Remaining Time \n", " 1 2870.9439 2.38m\n", " 2 2870.8054 2.37m\n", " 3 2870.7081 2.40m\n", " 4 2869.6915 2.40m\n", " 5 2869.0260 2.40m\n", " 6 2868.7040 2.38m\n", " 7 2868.3893 2.37m\n", " 8 2868.1410 2.36m\n", " 9 2867.9482 2.35m\n", " 10 2867.7302 2.34m\n", " 20 2866.5036 2.27m\n", " 30 2862.5196 2.14m\n", " 40 2860.7919 2.01m\n", " 50 2857.2792 1.90m\n", " 60 2856.3757 1.79m\n", " 70 2851.8679 1.66m\n", " 80 2849.5281 1.54m\n", " 90 2846.7930 1.42m\n", " 100 2844.0305 1.29m\n", " 200 2830.1153 0.00s\n", "0.5\n", " Iter Train Loss Remaining Time \n", " 1 4692.0647 2.61m\n", " 2 4678.8259 2.64m\n", " 3 4667.3195 2.58m\n", " 4 4658.5275 2.56m\n", " 5 4649.6677 2.52m\n", " 6 4642.8820 2.48m\n", " 7 4636.9898 2.46m\n", " 8 4631.8154 2.43m\n", " 9 4626.1916 2.41m\n", " 10 4619.1359 2.40m\n", " 20 4598.4591 2.27m\n", " 30 4593.3814 2.13m\n", " 40 4588.2154 1.99m\n", " 50 4583.3671 1.85m\n", " 60 4578.0011 1.73m\n", " 70 4573.5810 1.61m\n", " 80 4569.7910 1.49m\n", " 90 4566.1793 1.37m\n", " 100 4562.6173 1.25m\n", " 200 4536.8804 0.00s\n", "0.7\n", " Iter Train Loss Remaining Time \n", " 1 6488.9940 2.95m\n", " 2 6434.5371 2.94m\n", " 3 6397.0718 2.90m\n", " 4 6355.7493 2.88m\n", " 5 6321.0080 2.83m\n", " 6 6291.4892 2.82m\n", " 7 6269.4393 2.81m\n", " 8 6251.7225 2.80m\n", " 9 6238.1897 2.78m\n", " 10 6227.4985 2.77m\n", " 20 5840.2182 2.68m\n", " 30 5743.4240 2.60m\n", " 40 5705.0136 2.46m\n", " 50 5692.1113 2.30m\n", " 60 5685.9822 2.15m\n", " 70 5680.2777 2.01m\n", " 80 5675.6369 1.87m\n", " 90 5671.0865 1.71m\n", " 100 5666.9214 1.55m\n", " 200 5643.8790 0.00s\n", "0.9\n", " Iter Train Loss Remaining Time \n", " 1 7563.8009 2.44m\n", " 2 7353.6364 2.42m\n", " 3 7161.3795 2.42m\n", " 4 6904.6536 2.50m\n", " 5 6683.4869 2.53m\n", " 6 6496.3361 2.55m\n", " 7 6323.7878 2.58m\n", " 8 6184.3325 2.59m\n", " 9 6057.4769 2.59m\n", " 10 5946.5049 2.59m\n", " 20 5298.2247 2.41m\n", " 30 5083.7560 2.29m\n", " 40 4997.9081 2.17m\n", " 50 4892.4644 2.04m\n", " 60 4821.2919 1.90m\n", " 70 4783.5055 1.79m\n", " 80 4778.8681 1.68m\n", " 90 4772.9954 1.54m\n", " 100 4770.0468 1.39m\n", " 200 4709.8788 0.00s\n" ], "name": "stdout" } ] }, { "metadata": { "id": "H55y_74W97jH", "colab_type": "text" }, "cell_type": "markdown", "source": [ "## Keras\n", "\n", "From https://github.com/sachinruk/KerasQuantileModel/blob/master/Keras%20Quantile%20Model.ipynb\n", "\n", "One area that Deep Learning has not explored extensively is the uncertainty in estimates. However, as far as decision making goes, most people actually require quantiles as opposed to true uncertainty in an estimate. eg. For a given age the weight of an individual will vary. What would be interesting is the (for arguments sake) the 10th and 90th percentile. The uncertainty of the estimate of an individuals weight is less interesting." ] }, { "metadata": { "id": "FcPl_HNl9bzY", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "def tilted_loss(q, y, f):\n", " e = (y - f)\n", " return keras.backend.mean(keras.backend.maximum(q * e, (q - 1) * e), \n", " axis=-1)" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "FUGzb8LAY2TI", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "optimizer = tf.train.AdamOptimizer(0.001)\n", "early_stop = keras.callbacks.EarlyStopping(monitor='val_loss', patience=20)" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "yaR-Nnep2t7Z", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "sess = tf.Session()\n", "#tf.reset_default_graph()" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "3QoChH3zXVnl", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "def keras_pred(x_train, train_labels, x_test, q):\n", " print(q)\n", "# optimizer = tf.train.AdamOptimizer(0.001)\n", "# early_stop = keras.callbacks.EarlyStopping(monitor='val_loss', patience=20)\n", " # Set input_dim for the number of features.\n", " if len(x_train.shape) == 1:\n", " input_dim = 1\n", " else:\n", " input_dim = x_train.shape[1]\n", " model = keras.Sequential([\n", " keras.layers.Dense(UNITS, activation=tf.nn.relu,\n", " input_dim=input_dim),\n", " keras.layers.Dense(UNITS, activation=tf.nn.relu),\n", " keras.layers.Dense(1)\n", " ])\n", " \n", " model.compile(loss=lambda y, f: tilted_loss(q, y, f), optimizer=optimizer)\n", " model.fit(x_train, train_labels, epochs=EPOCHS, batch_size=BATCH_SIZE,\n", " verbose=0, validation_split=0.2, callbacks=[early_stop])\n", " \n", " # Predict the quantile\n", " return model.predict(x_test)" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "V8TX2Mn8wHVX", "colab_type": "code", "colab": { "base_uri": "https://localhost:8080/", "height": 102 }, "outputId": "009745d7-e52d-4412-eadb-66d27bc0e4d3" }, "cell_type": "code", "source": [ "preds.loc[preds.method == 'Keras', 'pred'] = np.concatenate(\n", " [keras_pred(X_train, y_train, X_test, q) \n", " for q in QUANTILES])" ], "execution_count": 46, "outputs": [ { "output_type": "stream", "text": [ "0.1\n", "0.3\n", "0.5\n", "0.7\n", "0.9\n" ], "name": "stdout" } ] }, { "metadata": { "id": "PEy2M6X89tbD", "colab_type": "text" }, "cell_type": "markdown", "source": [ "## TensorFlow\n", "\n", "Adapted from https://github.com/strongio/quantile-regression-tensorflow/blob/master/Quantile%20Loss.ipynb" ] }, { "metadata": { "id": "rpC7QNgqAaRE", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "# Initialize session\n", "tf.reset_default_graph()\n", "sess = tf.Session()" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "UlIlyNTIZqed", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "# Create network\n", "class q_model:\n", " def __init__(self, \n", " sess,\n", " quantiles,\n", " in_shape=1, \n", " out_shape=1, \n", " batch_size=32):\n", " \n", "# tf.reset_default_graph()\n", " \n", " self.sess = sess\n", " \n", " self.quantiles = quantiles\n", " self.num_quantiles = len(quantiles)\n", " \n", " self.in_shape = in_shape\n", " self.out_shape = out_shape\n", " self.batch_size = batch_size\n", " \n", " self.outputs = []\n", " self.losses = []\n", " self.loss_history = []\n", " \n", " self.build_model()\n", " \n", " def build_model(self, scope='q_model', reuse=tf.AUTO_REUSE): \n", " with tf.variable_scope(scope, reuse=reuse) as scope:\n", " self.x = tf.placeholder(tf.float32, shape=(None, self.in_shape))\n", " self.y = tf.placeholder(tf.float32, shape=(None, self.out_shape))\n", "\n", " self.layer0 = tf.layers.dense(self.x, \n", " units=UNITS, \n", " activation=tf.nn.relu)\n", " self.layer1 = tf.layers.dense(self.layer0, \n", " units=UNITS,\n", " activation=tf.nn.relu)\n", "\n", " # Create outputs and losses for all quantiles\n", " for i, q in enumerate(self.quantiles):\n", " # Get output layers \n", " output = tf.layers.dense(self.layer1, self.out_shape,\n", " name=\"{}_q{}\".format(i, int(q * 100)))\n", " self.outputs.append(output)\n", " \n", " # Create losses\n", " error = tf.subtract(self.y, output)\n", " loss = tf.reduce_mean(tf.maximum(q * error, (q - 1) * error),\n", " axis=-1)\n", "\n", " self.losses.append(loss)\n", "\n", " # Create combined loss\n", " self.combined_loss = tf.reduce_mean(tf.add_n(self.losses))\n", " self.train_step = tf.train.AdamOptimizer().minimize(\n", " self.combined_loss)\n", "\n", " def fit(self, x, y, epochs=EPOCHS):\n", " for epoch in range(epochs):\n", " epoch_losses = []\n", " for idx in range(0, x.shape[0], self.batch_size):\n", " batch_x = x[idx : min(idx + self.batch_size, x.shape[0]), :]\n", " batch_y = y[idx : min(idx + self.batch_size, y.shape[0]), :]\n", "\n", " feed_dict = {self.x: batch_x,\n", " self.y: batch_y}\n", "\n", " _, c_loss = self.sess.run([self.train_step, self.combined_loss],\n", " feed_dict)\n", " epoch_losses.append(c_loss)\n", " \n", " epoch_loss = np.mean(epoch_losses)\n", " self.loss_history.append(epoch_loss)\n", " if epoch % 10 == 0:\n", " print(\"Epoch {}: {}\".format(epoch, epoch_loss))\n", " \n", " def predict(self, x): \n", " # Run model to get outputs\n", " feed_dict = {self.x: x}\n", " predictions = sess.run(self.outputs, feed_dict)\n", " \n", " return predictions" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "2n7hPnDU__Yd", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "# Instantiate model\n", "tf_model = q_model(sess, quantiles=QUANTILES, in_shape=X_train.shape[1],\n", " out_shape=1, batch_size=BATCH_SIZE)\n", "\n", "# Initialize all variables\n", "init_op = tf.global_variables_initializer()\n", "sess.run(init_op)" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "6zX3wO8tAXH6", "colab_type": "code", "colab": { "base_uri": "https://localhost:8080/", "height": 51 }, "outputId": "b233db60-fc7e-4825-b2e4-f749de18ee58" }, "cell_type": "code", "source": [ "# Run training\n", "tf_model.fit(np.array(X_train), y_train_expanded, EPOCHS)" ], "execution_count": 50, "outputs": [ { "output_type": "stream", "text": [ "Epoch 0: 21430.86328125\n", "Epoch 10: 15456.2646484375\n" ], "name": "stdout" } ] }, { "metadata": { "id": "YBuUtIhA2FZm", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "preds.loc[preds.method == 'TensorFlow', 'pred'] = \\\n", " np.array([item for sublist in tf_model.predict(X_test)\n", " for item in sublist])" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "42LIBXl933YI", "colab_type": "text" }, "cell_type": "markdown", "source": [ "## Compare quantile loss" ] }, { "metadata": { "id": "NwrasOq8ClOJ", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "# pandas version rather than Keras.\n", "def quantile_loss(q, y, f):\n", " e = (y - f)\n", " return np.maximum(q * e, (q - 1) * e)" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "LKbkvlvm4p6s", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "preds['quantile_loss'] = quantile_loss(preds.q, preds.label, preds.pred)" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "2xXUGt4TKZsj", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "def plot_loss_comparison(preds):\n", " overall_loss_comparison = preds[~preds.quantile_loss.isnull()].\\\n", " pivot_table(index='method', values='quantile_loss').\\\n", " sort_values('quantile_loss')\n", " # Show overall table.\n", " print(overall_loss_comparison)\n", " \n", " # Plot overall.\n", " with sns.color_palette('Blues', 1):\n", " ax = overall_loss_comparison.plot.barh()\n", " plt.title('Total quantile loss', loc='left')\n", " sns.despine(left=True, bottom=True)\n", " plt.xlabel('Quantile loss')\n", " plt.ylabel('')\n", " ax.legend_.remove()\n", " \n", " # Per quantile.\n", " per_quantile_loss_comparison = preds[~preds.quantile_loss.isnull()].\\\n", " pivot_table(index='q', columns='method', values='quantile_loss')\n", " # Sort by overall quantile loss.\n", " per_quantile_loss_comparison = \\\n", " per_quantile_loss_comparison[overall_loss_comparison.index]\n", " print(per_quantile_loss_comparison)\n", " \n", " # Plot per quantile.\n", " with sns.color_palette('Blues', 7):\n", " ax = per_quantile_loss_comparison.plot.barh()\n", " plt.title('Quantile loss per quantile', loc='left')\n", " sns.despine(left=True, bottom=True)\n", " handles, labels = ax.get_legend_handles_labels()\n", " plt.xlabel('Quantile loss')\n", " plt.ylabel('Quantile')\n", " # Reverse legend.\n", " ax.legend(reversed(handles), reversed(labels));" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "tSvkJkbfQXE6", "colab_type": "code", "colab": { "base_uri": "https://localhost:8080/", "height": 2213 }, "outputId": "dbe15b51-0bd5-4406-856e-9932ad7f2a97" }, "cell_type": "code", "source": [ "plot_loss_comparison(preds)" ], "execution_count": 136, "outputs": [ { "output_type": "stream", "text": [ " quantile_loss\n", "method \n", "Random forests 1780.631185\n", "Keras 2902.365968\n", "TensorFlow 2947.832552\n", "Gradient boosting 3714.276605\n", "LogitOLS 4143.752395\n", "QuantReg 4344.568016\n", "OLS 11349.309620\n", "method Random forests Keras TensorFlow Gradient boosting \\\n", "q \n", "0.1 733.596181 1001.585328 988.429851 1001.582703 \n", "0.3 1582.886857 2314.623860 2355.565532 2796.654666 \n", "0.5 2109.426515 3460.318307 3408.195883 4502.006050 \n", "0.7 2404.227426 4078.920450 4150.995083 5600.271240 \n", "0.9 2073.018947 3656.381897 3835.976413 4670.868368 \n", "\n", "method LogitOLS QuantReg OLS \n", "q \n", "0.1 1035.972781 1001.582703 9589.040988 \n", "0.3 2931.184005 2836.598634 12109.529109 \n", "0.5 4460.544050 4664.776094 7560.337541 \n", "0.7 5826.730336 6360.021823 15555.600464 \n", "0.9 6464.330806 6859.860824 11932.040000 \n" ], "name": "stdout" }, { 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"text/plain": [ "" ] }, "metadata": { "tags": [] } } ] }, { "metadata": { "id": "N_WYiyyfN_ZE", "colab_type": "text" }, "cell_type": "markdown", "source": [ "Examine individual predictions." ] }, { "metadata": { "id": "PO1czqfSN-6-", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "worst_logitols = preds[preds.method == 'LogitOLS'] \\\n", " .sort_values('quantile_loss', ascending=False).head(1)\n", "worst_logitols_ix = worst_logitols['ix'].values[0]\n", "worst_logitols_label = worst_logitols['label'].values[0]" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "ApGeT5nQL0S8", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "example = preds[(preds['ix'] == worst_logitols_ix) &\n", " (preds.method.isin(['OLS', 'LogitOLS', 'Random forests']))]" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "-q11hTbqMQdP", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "example_pivot = example.pivot_table('pred', 'q', 'method')" ], "execution_count": 0, "outputs": [] }, { "metadata": { "id": "FMjWTsiqTLDS", "colab_type": "code", "colab": { "base_uri": "https://localhost:8080/", "height": 940 }, "outputId": "4835c128-b6f9-46e1-be88-b5915c7ca1d4" }, "cell_type": "code", "source": [ "with sns.color_palette('Blues', 3):\n", " example_pivot.plot()\n", " sns.despine(left=True, bottom=True)\n", " plt.title('Inverse CDF by method: RECID ' + worst_logitols_ix.astype(str),\n", " loc='left', y=1.04)\n", " plt.axhline(worst_logitols_label, color='gray', ls='dashed')" ], "execution_count": 203, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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L07FjR+GkX9XJdWkzMTFBr169hODctWvXFC4xUWbBggXCz7h169Yqj42Pjxe2tbS0FLZX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qm8vFxbt25Vfn6+8vPzna6ZPHmyZs+e3fVPBgAAAAA86G9ZR1Xb5DiFkhgdokXTBnipI8B/9MgQ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\nGQAAAwshCgAAwCBW3dCi7/zbDn14sNqyf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